Question: Simplify the following expression: $\dfrac{63y^3}{35y^5}$ You can assume $y \neq 0$.
$ \dfrac{63y^3}{35y^5} = \dfrac{63}{35} \cdot \dfrac{y^3}{y^5} $ To simplify $\frac{63}{35}$ , find the greatest common factor (GCD) of $63$ and $35$ $63 = 3 \cdot 3 \cdot 7$ $35 = 5 \cdot 7$ $ \mbox{GCD}(63, 35) = 7 $ $ \dfrac{63}{35} \cdot \dfrac{y^3}{y^5} = \dfrac{7 \cdot 9}{7 \cdot 5} \cdot \dfrac{y^3}{y^5} $ $\phantom{ \dfrac{63}{35} \cdot \dfrac{3}{5}} = \dfrac{9}{5} \cdot \dfrac{y^3}{y^5} $ $ \dfrac{y^3}{y^5} = \dfrac{y \cdot y \cdot y}{y \cdot y \cdot y \cdot y \cdot y} = \dfrac{1}{y^2} $ $ \dfrac{9}{5} \cdot \dfrac{1}{y^2} = \dfrac{9}{5y^2} $